Electronic structure methods permit the computational modeling of biomolecular systems from first principles of quantum mechanics without any experimental input or empiricism. This predictive capability comes at high computational cost, which restricts their use to key classes of problems where simpler empirical methods fail, such as making and breaking chemical bonds in reactions, or providing the first principles input to calibrate empirical force fields. This proposal aims to significantly enhance the performance of the most widely used electronic structure methods, such as second order perturbation theory, density functional theory, novel hybrids of the two, and some more advanced correlation methods. The opportunity is to gain a speedup of between 5 and 10 or more by developing dual basis approximations, a promising perturbative approach whose feasibility was established in the preliminary research. Its capabilities will be fully developed to permit force evaluation in addition to energies themselves. Other complementary algorithms that accelerate large-basis calculations on large molecules will also be formulated and implemented. This project aims to improve the efficiency of the most-widely used quantum chemistry models, namely density-functional theory and second-order perturbation theory. These methods are at the core of molecular modeling and applied widely in biological research/development and in drug discovery. The improvement will significantly increase researchers'productivity and extend its application scope.